Abstract

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl-Titchmarsh half-line m-coefficients (and 2 × 2 matrix-valued M-matrices) in the non-self-adjoint context and derive some of their basic properties. We conclude with an illustrative example showing that crossing spectral arcs in the non-self-adjoint context imply the blowup of the norm of spectral projections in the limit where the crossing point is approached.

Department(s)

Mathematics and Statistics

Sponsor(s)

National Science Foundation (U.S.)

Keywords and Phrases

Dirac Operators; J-Self-Adjointness; Spectral Theory

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2006 American Mathematical Society, All rights reserved.

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